Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Chemical Engineering Department MODELING AND SIMULATION OF FCC RISERS A RESEARCH SUBMITTED TO THE CHEMICAL ENGINEERING DEPARTMENT OF THE UNIVERSITY OF TECHNOLOGY IN THE PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF HIGHER DIPLOMA IN CHEMICAL ENGINEERING (PETROLEUM REFINING AND GAS TECHNOLOGY) By WALEED KHALID FADHIL B.Sc. in Chem. Eng. 1998 March 2012 08 Dedicated to My Family With My Deep Love FCC riser Plug flow reactor VGO feed Light gases Gasoline Coke Four lumps model . . UOP , . MxR chamber , . worksheet . I II ACKNOWLEDGMENTS First of all, thanks to Allah, who enabled me to achieve this research. I wish to express my sincere gratitude and thankfulness to my supervisor Dr. Shakir M. Ahmed for his kind supervision and continuous advices during the research. My grateful thanks to Prof. Dr. Mumtaz A. Zablouk, the Chairman of the Department of Chemical Engineering at the University of Technology for the provision of research facilities. Special thanks to Assist. Prof. Dr. Mohammed F. Abid for his help and support. I would like to express my sincere appreciation to Assis. Lec. Farooq A. Mehdi for his help. Also, my respectful regards to all the staff of Chemical Engineering Department of University of Technology. And finally my special thanks to my family for their support and encouragement. III ABSTRACT In the present work a mathematical model for the riser reactor of Fluid Catalytic Cracking has been developed. The riser is considered as a plug flow reactor incorporating the four lumps model for kinetics of cracking reactions. Catalyst deactivation function is calculated based on linear relationship between the catalyst coke content and its retention activity. The model has been validated using the plant data of a commercial FCC unit with RxCat technology developed by UOP. The model can predict the mixing temperatures, at MxR chamber and riser inlet; also shows the physical performance and productivity all over the riser height. An interactive excel worksheet is constructed and used as a powerful tool for solving the model equations and studying the effect of any change in operating variableson the unit performance. IV CONTENTS Certification I Acknowledgements III Abstract IV Contents V List of Figures VII List of Tables IX Nomenclature X CHAPTER - 1Introduction 1 1.1. Introduction 1 1.2. Aim and scope of Work 4 CHAPTER - 2Literature Survey 5 CHAPTER - 3Mathematical Modeling 10 3.1. Introduction 10 3.2. Reactor / Regenerator Material & Energy Balances 10 3.2.1. Material Balance 11 3.2.1.1. Reactor Material Balance 11 3.2.1.2. Regenerator Materials Balance 12 3.2.2. Energy Balance 13 3.2.2.1. Reactor Energy Balance 3.2.2.2. Regenerator Energy balance 3.3. 13 13 Riser model 14 3.3.1. Model Assumptions 14 3.3.2. Cracking Reaction Kinetics 15 3.3.3. Concentration, Temperature, Pressure and Coking time Profiles in the Riser 17 3.3.4. Catalyst Deactivation 18 3.3.5. Riser Hydrodynamics 19 V 3.3.6. Mixing Temperatures 21 3.4. Heat of Combustion at the Regenerator 23 3.5. Model Solution 23 CHAPTER - 4 Results and Discussion 26 4.1. Introduction 26 4.2. Case Study 26 4.3. Model Results 28 CHAPTER - 5 Conclusions and Recommendations 38 5.1. Conclusion 38 5.2. Recommendations for FutureWork 39 Appendix A -Fluidized Catalytic Cracking Technologies A-1 Appendix B - Variables of FCCunits B-1 Appendix C - Computer Programs C-1 Appendix D -Glossary of Terms Used In This Work E-1 References R-1 VI LIST OF FIGURES Figure No. Title Page No. Figure 1.1 Fluid Catalytic Cracking Unit 2 Figure 3.1 schematic of FCCU reactor/regenerator system used in present model 11 Figure 3.2 12 Figure 3.3 Input and output streams for reactor and regenerator in FCCU A volume element in the riser reactor Figure 3.4 Schematic of four lumped reactions 16 Figure 3.5 Mathematical representation of reactor riser used in the model 21 Figure 3.6 25 Figure 4.1 computational flow diagrams for riser reactor model Four lump concentration profile vs. riser height Figure 4.2 Riser temperature profile 28 Figure 4.3 Riser pressure profile 30 Figure 4.4 Gas phase molecular weight vs. riser length 30 Figure 4.5 Gas phase density vs. riser height 30 Figure 4.6 Gas phase mass rate vs. riser height 31 Figure 4.7 Slip factor vs. riser height 32 Figure 4.8 Gas phase and catalyst velocities vs. riser height Gas phase and catalyst residence times vs. riser height Gas phase void fraction vs. riser height 32 Figure 4.9 Figure 4.10 VII 14 28 33 34 Figure No. Title Page No. Figure 4.11 Predicted catalyst activity along the riser height 34 Figure 4.12 Gasoline yield vs. feed conversion 35 Figure 4.13 Feed conversion vs. riser height 35 Figure A-1(a) Stacked Reactor regenerator configuration A-2 Figure A-1(b) Side by side Reactor regenerator configuration A-2 Figure A-2 KBR's counter-current regeneration design A-5 Figure A-3 Lummus FCCU Process Flow Diagram A-7 Figure A-4 S&W / IFP FCCU design A-10 Figure A-5 Mix zone temperature control & Feed injection nozzle A-11 Figure A-6 Shell's FCC & MILOS-FCC designs A-13 Figure A-7 A-14 Figure A-8 PentaFlow Packing & Feed nozzels configurations UOP's reactor/regenerator FCCU design Figure B-1 FCC reaction network B-4 Figure B-2 Principal Reactions in Fluid Catalytic Cracking B-5 Figure B-3 Evolution in structure of FCC catalysts before 1990 Catalyst activity retention vs. Carbon on regenerated catalyst Constructed Excel worksheet For FCC unit B-6 Figure B-4 Figure C-1 VIII A-16 B-8 C-8 LIST OF TABLES Table No. Title Page No. Table 1.1 Gasoline Pool Example 2 Table 4.1 Kinetic parameters with Modified frequency factors used in present model 27 Table 4.2 Mixing temperatures at MxR chamber and Riser inlet temperature 27 Table 4.3 Model predicted and plant values comparison 36 Table 4.4 Case study results 36 Table A-1 KBR & ExxonMobil FCCU Technologies A-6 Table A-2 LUMMUS FCCU Technologies A-8 Table A-3 S&W / IFP FCCU Technologies A-11 Table A-4 Shell's FCCU Technologies A-14 Table B-1 Feedstock Crackability B-2 Table B-2 Typical FCC unit products B-3 Table B-3 Effect of operating Temperature of the reactor on the performance of a fluidized bed cracking B-11 Table C-1 Variables used in Polymath program C-1 IX NOMENCLATURES A Riser cross section area (m2) Ar Archimedes number (-) Cp Heat capacity (kJ/kg.K) D Riser diameter (m) d Particle diameter (m) Ej Activation energy (kJ/kmole) Fr Fround number H Heat enthalpy (kJ/s) Hj Heat enthalpy of jth reaction (kJ/kg) Kj Kinetic reaction rate constant of jth reaction Koj frequency factor or preexponential factor for jth reaction Kuop UOP characterization factor L Riser Height (m) MW Molecular weight (kg/kg mole) m Mass rate (kg/s) P Riser pressure (Pascal) R Universal ideal gas constant (atm m3/kmole K) Re Reynold number S Sulfur (kg/s) Sph Sphericity SG Feed specific gravity T Temperature (K) t Gas phase residence time (second) tc Catalyst residence time (second) u Velocity (m/s) WHSV Weighted hourly space velocity (1/hr) X Conversion (wt %) yi Weight fraction of ith lump X z Axial position of riser height (m) Greek letters Voidage Catalyst deactivation function Density (kg/m3) Slip factor Catalytic cracker efficiency Difference Viscosity (Pa.s) j Ratio of frequency factor of jth lump reaction per frequency factor of VGO to gasoline reaction Subscripts air Air for regeneration cok Coke cat Catalyst ds Dispersion or Atomizing steam f Feed fg Flue gas fl Feed in the liquid phase fv Feed in the vapor phase g Gas phase in Flowing in j 1,2,3,4 and 5 for the reactions VGO to GLN, VGO to LGS, VGO to COK, GLN to LGS, and GLN to COK respectively ls Lifting steam mix1 Mixing temperature at MxR chamber mix2 Mixing temperature at riser inlet XI o Superficial out Flowing out p Particle pr Products rcat Regenerated catalyst rcoke Coke on the regenerated catalyst s Steam si Riser and reactor inlet steam so Riser and reactor outlet steam scat Spent catalyst scok Coke on the spent catalyst t Terminal velocity xcat Carbonized catalyst xcok Coke of carbonized catalyst Abbreviations AF Advanced Fluidization BPSD Barrel Per Stream Day CB & I Chicago Bridge & Iron CCR Conradson Carbon Residue or Catalyst Circulation Rate CFD Computational Fluid Dynamics COK Coke CRC Coke on the Regenerated Catalyst CSC Coke on the Spent Catalyst C/O Catalyst to Oil ratio E-cat Equilibrium Catalyst EMRE ExxonMobil Research and Engineering FCC Fluidized Catalytic Cracking FCCU Fluidized Catalytic Cracking FEED Front End Engineering Design XII FF Fresh Feed GLN Gasoline HCO Heavy Cycle Oil IFP Institute France Petrol KBR Kellogg Brown & Root LCO Light Cycle Oil LGS Light Gases LPG Liquefied Petroleum Gas MTC Mix Temperature Control RON Research Octane Number RSS Riser Separator Stripper ODE Ordinary Differential Equation TSS Third Stage Separator UOP Universal Oil Products VDS Vortex Disengaging System VGO Vacuum Gasoil VSS Vortex Separation System XIII CHAPTER ONE INTRODUCTION Chapter One 1.1. Introduction INTRODUCTION Fluid catalytic cracking (FCC) technology is a technology with more than 60 years of commercial operating experience. The process is used to convert higher-molecular-weight hydrocarbons to lighter, more valuable products through contact with a powdered catalyst at appropriate conditions. The primary purpose of the FCC process has been to produce gasoline, distillate, and C3/C4 olefins from low-value excess refinery gas oils and heavier refinery streams. FCC is often the heart of a modern refinery because of its adaptability to changing feedstocks and product demands and because of high margins that exist between the FCC feedstocks and converted FCC products. As oil refining has evolved over the last 60 years, the FCC process has evolved with it, meeting the challenges of cracking heavier, more contaminated feedstocks, increasing operating flexibility, accommodating environmental legislation, and maximizing reliability [1] . In the environmental protection field, FCC unit play a significant role by producing the gasoline with lower benzene content as clarified in the gasoline pool example (Table 1.1) Refineries use fluid catalytic cracking to correct the imbalance between the market demand for gasoline and the excess of heavy high boiling range products resulting from the distillation of crude oil. [2] The fluid catalytic cracking (FCC) unit consists of a reaction section and a fractionating section that operate together as an integrated processing unit. The reaction section includes two reactors, the riser reactor, where almost all the endothermic cracking reactions and coke deposition on the catalyst occur, and the regenerator reactor, where air is used to burn off the accumulated coke. The regeneration process provides, in addition to reactivating the catalyst powders, the heat required by the endothermic cracking reactions, (Figure 1.1). [3] 1 Chapter One Introduction Figure 1.1: Fluid Catalytic Cracking Unit [4] Table 1.1 Gasoline Pool Example [5, 6] Gasoline source FCC Reformate Alkylate Isomerate % vol. of Pool % vol. Bz. RON 35 30 20 15 0.8 4.5 0 0.6 88 94 94 89 2 % vol Pool RON 33.8 31 20.6 14.6 Reformer Alkylation FCCU Isomerization Chapter One Introduction A modern FCC unit comprises different sections such as a riser reactor, a stripper, a disengager, a regenerator, a main fractionator, catalyst transport lines (spent catalyst standpipe and regenerated catalyst standpipe) and several other auxiliary units such as: cyclones, air blower, expander, wet gas compressor, feed pre-heater, air heater, catalyst cooler, etc [7] . The proprietary new designs and technologies that have been developed by the major FCC designers and licensors are briefly described in the Appendix A. Because of the importance of FCC unit in refining, a construction of mathematical model that can describe the dynamic behavior of FCC unit equipments in steady state is very important. Accurate model can be used as a powerful tool to study the effect of process variables on the performance and productivity of the system [7]. Simulation studies also provide guidance in the development of new processes and can reduce both time and investment [8] . The effective simulation of the fluid catalytic cracking operation requires knowledge of reaction kinetics, fluid dynamics, feed and catalyst effects [9]. The riser reactor is probably the most important equipment in a FCC unit. The modeling of a riser reactor is very complex due to complex hydrodynamics and unknown multiple reactions, coupled with mass transfer resistance, heat transfer resistance and deactivation kinetics. A complete model of the riser reactor should include all the important physical phenomena and detailed reaction kinetics [10]. 3 Chapter One 1.2. Introduction AIMS AND SCOPE OF WORK The main objectives of the present work are: 1. A short literature review of previous FCC riser modeling and simulation studies. 2. Formulation of a mathematical model that can describe the reaction kinetics and physical performance in the riser section of FCC unit by using four lump model for kinetics description with linearly scaled up frequency factors of Arrhenius equations. 3. The quantities of lifting and dispersion steam in all calculation steps will be considered. 4. Model validation against a commercial scale FCC unit designed by UOP is to be investigated. 5. An interactive excel worksheet for solving model equations and studying the unit performance is to be constructed. 4 CHAPTER TWO LITERATURE SURVEY Chapter Two Literature Survey Modeling of riser reactor is very complex due to complex hydrodynamics, unknown multiple reactions coupled with mass transfer and heat transfer resistances. Also, the conditions keep changing all along the riser height due to cracking which causes molar expansion in the gas phase and influences the axial and radial catalyst density in the riser. In the literature, numerous models of FCC riser are available with varying degrees of simplifications and assumptions. Ali et al. (1997) [3] ; Arbel et al. (1995) [11] ; Han et al. (2001) [12] , developed a mathematical model of an industrial FCC unit, includes one dimensional mass, energy, and species balance; their models was based on the assumption of instantaneous and complete vaporization of the feed when contacted with hot regenerated catalyst assuming modern high efficiency feed injection systems. These types of modeling are normally simple to formulate and to solve. They are more suitable when the interest is to explore the influence of operating conditions, test a kinetic model or when the simulation includes not only the riser, but also other equipments like the regenerator and the stripper. The simplest kind of these models is the homogeneous version, where both the vapor phase (hydrocarbon feed & products vapors) and the solid phase (catalyst & coke) are moving at the same velocity. The heterogeneous version considers different velocities for the two phases, resulting in different residence times for each phase inside the riser. The simplest hydrodynamic models assume steady state ideal plug flow reactor. 5 Chapter Two Ali et al. Literature Survey [3] and Han et al. [12] used the four-lump kinetic models to describe the behavior of cracking reactions, while Arbel et al. [11] used more complex ten-lump model. Theologos and Markatos (1993) [13] proposed a three dimensional mathematical model considering two phase flow, heat transfer, and three lump reaction scheme in the riser reactor. The authors developed the full set of partial differential equations that describes the conservation of mass, momentum, energy and chemical species for both phases, coupled with empirical correlations concerning interphase friction, interphase heat transfer, and fluid to wall frictional forces. The model can predict pressure drop, catalyst holdup, interphase slip velocity, temperature distribution in both phases, and yield distribution all over the riser. Theologos et al. (1997) coupled the model of Theologos and Markatos (1993) [13] [14] with a ten lump reaction scheme to predict the yield pattern of the FCC riser reactor. An integrated dynamic model for the complete description of the fluid catalytic cracking unit (FCC unit) was developed by Bollas et al. (2002) [15] ; the model simulates successfully the riser and the regenerator of FCC and incorporates operating conditions, feed properties and catalyst effects. Erthal et al. (2003) [16], developed a one dimensional, mathematical model, they considered in their model gas-solid flow that occurs in FCC risers, two equations of momentum conservation applied to the compressible gas flow and solid flow respectively, the model considers also the drag force and heat transfer coefficient between two phases; four lump model used for cracking reactions description. 6 Chapter Two Literature Survey Souzaa et al. (2003) [17] , combined a 2-D fluid flow field with a 6- lumps kinetic model and used two energy equations (catalyst and gas oil) to simulate the gas oil cracking process inside the riser reactor. Das et al. (2003) [18] , performed the three-dimensional simulation of an industrial-scale fluid catalytic cracking riser reactor using a novel densitybased solution algorithm. The particle-level fluctuations are modeled in the framework of the kinetic theory of granular flow. The reactor model includes separate continuity equations for the components in the bulk gas and inside the solid phase. Berry et al. (2004) [19] , modified the two-dimensional hydrodynamic model to make it predictive by incorporating the slip factor for the calculation of the cross-sectionally averaged voidage. The model has been coupled with the four-lump kinetic model to predict the effect of operating conditions on profiles of conversion, yield, temperature and pressure in the riser. Hassan (2005) [20] , developed Material and energy balance calculations to design Fluidized catalytic cracking (FCC) unit from Iraqi crude oil. She used the visual basic program in her work. With regard to reaction and kinetics, Xu et al. (2006) [21] proposed a seven lump kinetic model to describe residual oil catalytic cracking, in which products especially coke were lumped separately for accurate prediction. Because in recent studies, kinetics was developed accounting for coke formation leading to catalyst deactivation. The reactor block is modeled as a combination of an ideal Plug Flow Reactor (PFR) and a Continuously Stirred Tank Reactor (CSTR). 7 Chapter Two Literature Survey On the other hand, Krishnaiah et al. (2007) [22], a steady state simulation for the fluid cracking was investigated, the riser reactor was modeled as a plug flow reactor incorporating four lump model for cracking reactions; they studied the effect of the operating variables on FCC unit performance, a catalyst to oil ratio, air rate and gasoil inlet temperature have been chosen as operating variables. Souza et al. (2007) [23] , bi - dimensional fluid flow combined with six lumps kinetic model and two energy equations are used to model the gasoil mixture flow and the cracking process inside the riser reactor. Gupta et al. (2007) [24] proposed a new kinetic scheme based on pseudocomponents cracking and developed a semi-empirical model for the estimation of the rate constants of the resulting reaction network. Fifty pseudocomponents (lumps) are considered in this scheme resulting in more than 10,000 reaction possibilities. The model can be easily used to incorporate other aspects of the riser modeling. Ahari et al. (2008) [25], a one dimensional adiabatic model for riser reactor of FCC unit was developed, the chemical reaction were characterized by a four lump kinetic model, in their study, four cases of industrial riser operating conditions have been adopted and the modified kinetic parameters are used to eliminate the deviations between calculated and real values, also simulation studies are performed to investigate the effect of changing process variables. Based on Ahari et al. (2008) [25] study, Heydari et al. (2010) [26] performed an excessive analysis to gasoline yield throughout the riser with respect to different inlet mixing temperatures, different feed rates and different catalyst to oil ratios. 8 Chapter Two Shakoor (2010) Literature Survey [27] developed a computer program using MATLAB 7 software to determine the rate constants of FCC unit cracking reactions represented by six lump model and at any certain temperature. Baurdez et al. (2010) [28] proposed a method for steady-state/transient, two phase gas-solid simulation of a FCC riser reactor. Authors used a simple four lump kinetic model to demonstrate the feasibility of the method Osman et al. (2010) [29] developed a kinetic model to simulate the riser of a residue fluid catalytic cracking unit (RFCC) at steady state. The model based on combination the material and energy balance equations with seven lump model and a modified two dimensional hydrodynamic model. Simulation has been performed based on the data from an operating unit at Khartoum Refinery Company (KRC). MATLAB environment has been used to solve and analyze the kinetic model and process variables. A control system of a fluidized-bed catalytic cracking unit has been developed by AL-Niami (2010) [30] . In this work the dynamic and control system based on basic energy balance in the reactor and regenerator systems have been carried out. For the control system, the important input variables were chosen to be the reactor temperature and the regenerator temperature. 9 CHAPTER THREE MATHEMATICAL MODELING Chapter Three 3.1. Mathematical Modeling INTRODUCTION In this chapter, a mathematical model for the riser of an industrial FCC is developed, based on the reactor/regenerator configuration presented in the Figure 3.1. The preheated raw oil and steam are introduced into the reactor riser at a point near the base of the riser above the MxR Chamber. Here, the feed is contacted with a controlled amount of regenerated catalyst and lift media from the MxR Chamber. The regenerated catalyst flow is controlled to maintain a desired reactor temperature, and the spent catalyst recirculation to the MxR Chamber is controlled manually or by ratio to the regenerated catalyst flow. Feed and steam are mixed and injected through the feed nozzles distributors. At the distributors the riser diameter increases to allow for the expansion of hydrocarbon vapors as the oil is vaporized when it meets the catalyst. As a result of feed vaporization, the cracking reactions start and the density of the oil decreases causing an increase in the velocity of the vapor/gas phase. The increasing gas phase velocity accelerates the velocity of the catalyst and the riser behaves as a transport bed reactor. The Gasoil is converted to gasoline range hydrocarbons, light gases and coke. The cracking reactions' by product (coke) gets deposited on the catalyst surface and decreases its activity as the catalyst moves toward the exit of the riser. Because the riser volume is small, it limits the contact time between the catalyst and hydrocarbon to 5 seconds or less, and prevents over cracking of the feed[10]. 3.2. REACTOR/REGENERATOR MATERIAL & ENERGY BALANCES The material and energy balances around the reactor and the regenerator can be calculated by defining the input and output streams (Figure 3.2). 10 Chapter Three Mathematical Modeling Figure 3.1 schematic of FCC unit reactor/regenerator system used in present model [31] 3.2.1. MATERIAL BALANCE The material balance for any system at steady state is defined as: Mass in = Mass out 3.2.1.1. REACTOR MATERIAL BALANCE Mass in = Mass of (feed + steam + regenerated catalyst) Mass out = Mass of (reactor vapor + spent catalyst + steam) Where, the oil feed contains small quantity of sulfur, portion of the sulfur goes with spent catalyst and burned to SO2 in the regenerator, the remainder exists with products; and steam inlet is equal to summation of lifting steam, injection steam and stripping steam. 11 Chapter Three Mathematical Modeling Assuming steam inlet does not condense and is present in the exit vapor products at the same rate, therefore reactor material balance can be expressed as[33]: mf + m si + mrcat = mpr + mso + mscat (3.1) Since, mscat = mrcat + mcokandm si = m so Then, eq. (3.1) eliminated to: mf = mpr + mcok (3.2) 3.2.1.2. REGENERATOR MATERIAL BALANCE Mass in = Mass of (spent catalyst + air for coke burning) Mass out = Mass of (flue gases + regenerated catalyst) OR mscat + mair = m fg + mrcat H Flue gases (mfg) Radiation losses (3.3) Reaction mscat H Product vapors + steam (mpr+mso) Radiation losses Combustion of Coke Heat removal mrcat Air (mair) FEED (mf) Steam (msi) Figure 3.2 Input and output streams for reactor and regenerator in FCCU 12 Chapter Three Mathematical Modeling 3.2.2. ENERGY BALANCE The hot regenerated catalyst supplies the bulk of the heat required to vaporize the liquid feed to provide the overall endothermic heat of cracking, and to raise the temperature of dispersion steam and inert gases to the reactor temperature. [40] The energy balance equation at steady state may be written as: Energy in + Energy produced = Energy out + Energy consumed 3.2.2.1. REACTOR ENERGY BALANCE Energy in = Energy of (feed + regenerated catalyst + steam) Energy produced =0 Energy out = Energy of (reactor vapors + spent catalyst + radiation losses) Energy consumed = Heat of reaction If the Reactor temperature is the reference base temperature, then -Hfeed - Hsteam + Hregenerated catalyst = H radiation losses + HReaction Or Hregenerated catalyst = Hfeed + H steam + Hradiation losses +HReaction (3.4) 3.2.2.2. REGENERATOR ENERGY BALANCE Energy in = Energy (air with moisture + spent catalyst + coke) Energy produced = Combustion heat of coke Energy out = Energy (flue gas with moisture + regenerated catalyst +removed by catalyst cooler + radiation losses) Energy consumed = 0 If the Regenerator temperature is the reference temperature then, Hcombustion of coke = Hcatalyst + Hair + Hsteam+ Hcoke+ H removed + H radiation losses (3.5) 13 Chapter Three Mathematical Modeling The enthalpy change for the spent and regenerated catalyst is given by Hspent catalyst = mcatCpcat(Regen. Temp.- Reactor Temp.) Hregenerated catalyst = mcatCp cat(Reactor Temp. -Regen. Temp.) At steady conditions, Hspent catalyst + Hregenerated catalyst = 0 3.3. RISER MODEL For numerical computation, riser is divided into equal sized segments of thickness (dz), forming sequential equal sized volume elements (see Figure 3.3). Z=L dz z Z=0 Figure 3.3 A volume element in the riser reactor 3.3.1. MODEL ASSUMPTIONS In order to develop a mathematical model for the riser reactor, the following assumptions are introduced: 14 Chapter Three Mathematical Modeling a. One dimensional transported plug flow reactor prevails in the riser without radial and axial dispersion b. Steady state operation c. The riser wall is adiabatic. d. Viscosities and heat capacities for all components in vapor phase are constant along the riser. e. The pressure change through the riser length is due to the static head of catalyst in the riser. f. The coke deposited on the catalyst does not affect the fluid flow g. Instantaneous vaporization occurred in entrance of riser. h. Each volume element is assumed to contain two phases (i) solid phase (catalyst and coke) and (ii) gas phase (vapors of feed and product hydrocarbon, and steam). i. Each volume element, solid and gas phases are assumed to be well mixed so that heat and mass transfer resistances can be ignored, and the two phases have the same temperature. j. The gas-solid flow is fully developed along all the riser height. 3.3.2. CRACKING REACTIONS KINETICS The FCC process involves a network of reactions producing a large number of compounds. Therefore, lumping models can be used to describe the reaction system in terms of the feed and a defined number of products, the agglomeration of many chemical compounds into a single compound (called a lump),should exhibit some or several common properties(i.e. boiling point, molecular weight, reactivity).In this work four lump model scheme has been selected (Figure 3.4). This scheme consists of (VGO feed, Light gases, Gasoline, and Coke), it is more realistic and simple to solve, with more lumps, the mathematic becomes more complicated. 15 Chapter Three Mathematical Modeling K2 Light gases K4 VGO K1 Gasoline K5 K3 Coke Figure 3.4 Schematic of four lumped reactions According to this scheme, a part of gasoline is also converted to light gases and coke. It is assumed that cracking reaction rate is second order with respect to Gasoil, and first order with respect to Gasoline, and the reactions take place only in the vapor phase[3]. Rate constants (Kj) for cracking reactions follow the Arrhenius dependence on temperature (equation 3.6). (3.6) = Where, the kinetic parameters (Koj and Ej) for cracking reactions are selected from the literatures[23, 25]. In order to fit the predicted gasoline yield with industrial gasoline yield, the selected frequency factors can be scaled linearly by dividing each one by the modified frequency factor (Ko1)ofthe reaction feedstock gasoline: = (3.7) While, the selected activation energies are used directly in the industrial scale unit model. This approach has been adopted by Ancheyta (2011) [34]. 16 Chapter Three Mathematical Modeling 3.3.3. CONCENTRATION, TEMPERATURE, PRESSURE AND COKING TIME PROFILES IN THE RISER In order to calculate the concentration profile for each lump throughout the riser height, a differential material balance can be applied along the riser, the following set of equations is obtained[3, 22, 33]: For VGO lump: For gasoline lump: = = For light gases lump: = For coke lump: = [ [ [ [ + ( + + + + ) (3.8) (3.9) (3.10) (3.11) The temperature profile along the riser can be calculated using following ( energy balance equation [3, 22, 33]: = + + + ) +( + ) (3.12) Where, the term {- [(K1H1+K2H2+K3H3) y12 + (K4H4+K5H 5) y2]} represents the energy absorbed by endothermic reaction of vapor phase in the riser [16]. The pressure change throughout the riser can be predicted by[34]: = (1 ) 17 (3.13) Chapter Three Mathematical Modeling The catalyst residence time can be calculated using following equation [33]: = +[ (1 ) (3.14) The variation of the vapor phase mass flow rate (m g) throughout the riser = ( + )+ + + can be predicted by the following equation [33]: (3.15) Where, the quantities of dispersion steam (mds) and lifting steam (mls) that inlets the riser are controlled as 1wt% and 3.5wt% of the feed rate, respectively. The vapor phase density considered ideal gas and calculated by: = 101325 1 (3.16) The average vapor phase molecular weight expressed as [16]: = + + + ( )/ (3.17) 3.3.4. CATALYST DEACTIVATION The catalyst deactivation function ( )due to coke deposition, generally, there are two ways of its representation, one that depends on the catalyst contact time and the other one depends on the catalyst coke content. Since the functions that depend on the contact time do not account for the efficiency of the regenerator, i.e. the catalyst activity at the riser inlet. Therefore, in this work a single deactivation function depending on the catalyst coke content has been formulated from (Figure B-4) in appendix B using curve fit technique: 18 Chapter Three = 1 45 ( Mathematical Modeling )+ (3.18) 3.3.5. RISER HYDRODYNAMICS After complete vaporization of feed, only solid phase (catalyst & coke) and vapor phase (steam, hydrocarbon feed and product vapor) are left. Based on the model assumption, the two phases in fully developed flow, the empirical correlation (equation 3.19) developed by Patience et al. (1992) for calculating slip factor can be applied. Slip factor, defined as the ratio of interstitial gas velocity to average solids velocity. Where And = = = = =1+ 5.6 + 0.47 . (3.19) (3.20) (3.21) = (3.22) The superficial gas velocity is calculated by: And the average particle velocity calculated by [25]: = (1 ) (3.23) By combination of equations (3.19),(3.22) and (3.23), the average void fraction of the vapor phase can be evaluated by: 19 Chapter Three = = Mathematical Modeling + Therefore, the gas and particle velocities can be evaluated by: = (3.24) (3.25) (3.26) The residence time of the gas phase can be represented as the ratio of = (3.27) distance and velocity as: In order to calculate the particle terminal velocity, many correlations used and can be found in the literatures. In general, the terminal velocity is usually calculated for three zones: Stokes, intermediate and Newton zone, and it classified according to Archimedes numbers which defines the border between different zones. The Stokes regime holds for Ar< 32.9, Intermediate regime is valid for 32.9 106.5. In this work the simple correlation (equation3.29) for intermediate regime has been employed for calculating Reynolds number based on particle terminal velocity[35, 36, 37]: = = 18 + (2.3348 1.7439 = 20 ) (3.28) . (3.29) (3.30) Chapter Three Mathematical Modeling 3.3.6. MIXING TEMPERATURES In order to calculate the mixing temperature (Tmix1) at the MxR chamber, where the hot regenerated catalyst is mixed with the carbonized catalyst which has the same riser outlet temperature, and the mixed catalysts are lifted by steam (Figure3.5). The energy balance around MxR chamber can be applied to obtain the following equation: = ( + ( + ) ) +( +( + + ) + ) ( ) (3.31) mg Tout mscat mscok Tout Regenerator mcat mcok mg Tmix2 Regenerated catalyst mds Tds mf Tfl API Cpfv mcat mcok mls Tmix1 m rcat m rcok Trcat MxR chamber mxcat mxcok Tout Carbonized catalyst (Lifting steam) mls Tls Figure 3.5 Mathematical representation of reactor riser used in the model 21 Chapter Three Mathematical Modeling For calculating the riser inlet mixing temperature (Tmix2), where the lifting (regenerated/carbonized catalysts + steam) are mixed with injected (feed + dispersion steam), the energy balance (equation3.32) around the riser inlet can be formulated. ( = [ 1(1.8 )+ ( ( ) + 2.32 459.67) 2(1.8 )+ ( 459.67) + 3 ) (3.32) Solving equation (3.32) for Tmix2, and taking the positive root for the quadratic equation gives: = Where = 2.32 3.24 = + 1 ( + 1 2.32 1.8 = 2.32 (459.67) + 4 2 + (3.33) 2 (3.34) 2.32 1654.812 1 + 2.32 459.67 3 2.32 + + ) (3.35) 2 + 2.32 (3.36) Note that equation (3.33) represents the initial boundary condition to the differential equation (3.12) 22 Chapter Three 3.4. Mathematical Modeling HEAT OF COMBUSTION AT THE REGENERATOR At the regenerator where coke on the catalyst is burning off, the heat consumed (kJ/s) for catalyst heating up inside the regenerator can be calculated: = ( ) (3.37) And the heat consumed (kJ/s) for heating up the coke, air and moisture plus heat losses and removed are assumed 38% of total heat of combustion of 1 0.38 the coke. Therefore, equation 3.5 becomes: = (3.38) Therefore, the heat of combustion at the regenerator per 1Kg of coke burnt, can be calculated as follows: 3.5. = . (3.39) MODEL SOLUTION A computer program presented in Appendix C for the model simulation was developed using polymath version 5.1 and Microsoft Excel worksheet 2007, based on the 4th order Runge - Kutta method numerical technique; and a sequential approach has been chosen in this solution. In the present work the height of each volume element was kept 5cm. Further decrease in the height of the volume element had no appreciable effect on the results. The sequence of calculation steps is listed below and the flow diagram for the same sequence is given in Fig. 3.6. The model results and discussions are presented in chapter four. 23 Chapter Three Mathematical Modeling Sequence of calculation steps: 1. Read the input data required for calculation of MxR chamber temperature. 2. Calculate Tmix1 (equation 3.31) 3. Read the input data required for calculation of riser inlet temperature. 4. Calculate Tmix2 (equation 3.33) 5. Read the input initial values of ODEs. 6. Calculate the variable parameters (, K1, K2, K3, K4, K5, MWg, g, mg, Uo, Ar, Ret, Ut, , g, U g, Up, X) using the appropriate correlations. In this step all the calculated variable parameters are represent the conditions of current volume element. As the conditions at the exit of current volume element are the same as the conditions at the inlet of the next volume element, therefore, use these calculated values as an initial values for calculation the next volume element conditions, equations (3.6) and (3.15) to (3.30). 7. Go to the next volume element with (z = z + 0.05). 8. Calculate the new values of ODEs depending on the calculated values in step 6, equations (3.8) to (3.14). 9. Repeat steps 6 - 8 until the sum of increment height equals the height of the riser. 10. Calculate the yields and conversion at the exit of the riser. 11. Calculate the cracking efficiency, selectivity, WHSV, delta coke, Hcombustion of coke. 24 Chapter Three Mathematical Modeling START INPUT mrcat , mrcok,Trcat , mxcat , m xcok , Tout , mls , Tls , Cpcat , Cp cok , Cp s From E. B. Calculate Tmix1, eq. (3.31) INPUT mf , Tf , Kuop , API , SG , mds , Tds , Cpg From E. B. Calculate Tmix2, eq. (3.33) Z=0 INPUT initial values of ODEs from (3.8) to (3.14) y1=1 , y2= y3= y4= 0 , tc= 0, T = Tmix2, P = Pin Calculated and updated values , K1, K2 , K3 , K4 , K5, MWg , g , mg , uo , Ar , Ret , ut , , g , ug , up , X, t Equations (3.6) and (3.15) to (3.30) Z = Z + 0.05 Solve above seven ODEs by Runge - Kutta method Z